Legia Warsaw missed two penalties but still managed to thrash 10-man Celtic 4-1 in another of the third qualifying round, first leg ties.
Salzburg, who have blasted 11 goals in their opening two league matches of the season, found life much tougher in Baku where they fell behind to a Danilo Dias goal after two minutes and had Christian Schwegler sent off just after the half hour.
The numbers were evened up when Qarabag captain Admir Teli was dismissed just before half-time after being booked twice in as many minutes.
Salzburg dominated the second half, finally equalising with a superb strike by Spaniard Jonathan Soriano in the 77th minute before hitting the bar shortly afterwards.
But Qarabag's chances of becoming the first Azeri team to reach the group stage were given an unexpected boost when Dias's fellow Brazilian Reynaldo took advantage of slack defending to snatch an 88th minute winner. Reynaldo was dismissed one minute later for a wild challenge.
The Russians had midfielder Axel Witsel sent off soon after.
Kazakhstan's FK Aktobe twice came from behind to draw 2-2 at home to former European champions Steaua Bucharest and APOEL Nicosia, trailing 2-0 at half-time, hit back to draw 2-2 at HJK Helsinki.
Bulgarian champions Ludogorets Razgrad were held to a 0-0 draw at home by their Serbian counterparts Partizan Belgrade while the Dnipro Dnipropetrovsk-FC Copenhagen and Standard Liege-Panathinaikos ties also ended goalless.
Croatian champions Dinamo Zagreb, attempting to reach the group stage for the fifth time, won 1-0 at Denmark's Aalborg when Marcelo Brozovic scored in the 49th minute.
It was a disappointing result for Aalborg after enthusiasm over their domestic form had seen shares in the club jump as much as 280 percent earlier in the day.
Damjan Bohar scored in the fifth minute of stoppage time as Maribor (Slovenia) beat Maccabi Tel Aviv (Israel) by the same score at home.
Sebastien Corchia and Ryan Mendes scored in each half as Lille beat Grasshoppers 2-0 away.
- Sports & Recreation
- Christian Schwegler
- Legia Warsaw
- Danilo Dias